# Circle A has a center at (3 ,2 ) and an area of 13 pi. Circle B has a center at (9 ,6 ) and an area of 28 pi. Do the circles overlap?

Feb 7, 2018

Circles Overlap

#### Explanation:

In Circle A $\pi {R}_{A}^{2} = {A}_{A} = 13 \pi$

${R}_{A} = \sqrt{\frac{\cancel{\pi} \cdot 13}{\cancel{\pi}}} = \sqrt{13}$

Similarly in Circle B, ${R}_{B} = \sqrt{\frac{\cancel{\pi} \cdot 28}{\cancel{\pi}}} = \sqrt{28}$

${R}_{A} + {R}_{B} = \sqrt{13} + \sqrt{28} \approx 8.8971$

Distance between the centers ${O}_{A} , {O}_{B}$

vec(O_AO_B) = sqrt(9-6)^2 + (6-2)^2) = sqrt52 ~~ 7.2111

Since $\vec{{O}_{A} {O}_{B}} < {R}_{A} + {R}_{B}$, both the circles overlap.